anonymous
  • anonymous
FAN+MEDAL+TESTIMONIAL:):)!! How many arrangements are there of the word MATHEMATICS? How many of these start with the letter M? How many of the arrangements in part a have the T’s together?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I think that this is a permutation problem. So given that there are 11 letters in the word math, I will do the following calculation
anonymous
  • anonymous
11P11
anonymous
  • anonymous
Without restrictions

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anonymous
  • anonymous
@nincompoop
anonymous
  • anonymous
hai
anonymous
  • anonymous
Hi Sir:)
anonymous
  • anonymous
Am I on the right track?
anonymous
  • anonymous
ya know I'm stuck on this question right now too :P
anonymous
  • anonymous
This is a university level math don't worryXD
anonymous
  • anonymous
:O really? its on my 8th grade quiz
anonymous
  • anonymous
Forgive me I am in a Canadian school.
anonymous
  • anonymous
lol ok i will try to help tho
anonymous
  • anonymous
gimee a sec
anonymous
  • anonymous
Arrangement of letters of a word is a permutation question right?
anonymous
  • anonymous
As opposed to combination
anonymous
  • anonymous
Hi everyone:)
anonymous
  • anonymous
Am I on the right track?
anonymous
  • anonymous
I don't know.
anonymous
  • anonymous
How many arrangements are there of the word MATHEMATICS? Rule: Start with the factorial of the number of letters in the word. Then, for each indistinguishable letter in the word, divide by the factorial of the number of times that letter occurs in the word. "MATHEMATICS" is an 11-letter word. If all the letters were distinguishable like in "MATHEmatICS", the answer would be 11! = 39916800 However, there are 2 indistinguishable M's 2 indistinguishable A's 2 indistinguishable T's Thus, using the rule, we divide 11! by (2!)(2!)(2!) \[\frac{ 11! }{ 2!*2!*2! }=\frac{ 39916800 }{ 8 }=4989600\] How many of these start with the letter M? That amounts to finding all the distinguishable arrangements of the 10-letter "word" "ATHEMATICS" and putting an M in the beginning of each. "ATHEMATICS" is a 10-letter "word" and it contains 2 indistinguishable A's 2 indistinguishable T's Thus, using the rule, we divide 10! by (2!)(2!) \[\frac{ 10! }{ 2!*2! }=\frac{ 3628800 }{ 4 }=907200\] How many of the arrangements in part a have the T’s together? That amounts to finding all the distinguishable arrangements of the 10-letter "word" "MATHEMAICS" and inserting another T to the right of the "T" in each. "MATHEMAICS" is a 10-letter "word" and it contains 2 indistinguishable M's 2 indistinguishable A's Thus, using the rule, it's exactly the same answer as the second part. We divide 10! by (2!)(2!) \[\frac{ 10! }{ 2!*2! }=\frac{ 3628800 }{ 4 }=907200\] There ya go!
anonymous
  • anonymous
YOU ROCK:)
anonymous
  • anonymous
:)
anonymous
  • anonymous
ok testimonial?
anonymous
  • anonymous
let me know if it could be better

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